The unknown physics of star formation and feedback represent the main bottleneck in connecting the observable galaxy population to cold dark matter cosmology. Both physical processes are expected to vary strongly with galactic environment and across cosmic history. I will discuss recent progress in understanding the physics of star formation and feedback in the inner few hundred pc of the Milky Way — the Central Molecular Zone (CMZ) — an environment with gas properties very similar to those in starbursts and high-z galaxies, in which most stars in the Universe formed. Within our lifetime, the CMZ is the only such environment for which it will be possible to simultaneously resolve the gas properties down to the size scales of individual (forming) stars, while also tracing galactic-scale processes, making it a critical benchmark for studies of star formation, feedback, and the interstellar medium across cosmic time. I will focus on recent work seeking to explain a puzzling observational paradox: the vast majority of gas in the CMZ is underproducing stars by 1-2 orders of magnitude compared to empirical star formation relations and theoretical predictions, and yet at the same time a very small fraction of the gas is producing the most violent star formation events in the Galaxy. I will discuss the implications of these findings for environmentally (in)dependent star formation relations and theories. I will finish by outlining the details of a model linking the emerging, multi-scale picture of star formation and feedback to a more general understanding of the mass flows and energy cycles in galactic nuclei.